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4"23%Recita,on%
Prof.%Gifford%L18%Analysis%of%Chroma,n%Structure%
1
Announcements%
• Problem%Set%5%due%next%Thursday%(May%1st)%• 2%more%lectures%from%Prof.%Gifford%(including%today),%then%2%guest%lectures%"%Ron%Weiss%from%MIT%(Synthe,c%Bio),%George%Church%from%Harvard%(Genome%Engineering%&%Systems%Biology)%
• 2nd%exam%–%Tuesday,%May%6th%
2
Outline%
• Chroma,n%Structure%
• Dynamic%Bayesian%Networks%/%Segway%
• DNAse"seq%&%Protein%Interac,on%Quan,ta,on%(PIQ)%
%• ChIA"PET%reveals%3D%interac,ons%in%the%genome%
3
Introduc,on%to%Chroma,n%• DNA%in%one%cell%is%3%meters%long,%yet%fits%into%a%,ny%nucleus%• To%facilitate%the%packaging,%DNA%is%wrapped%around%nucleosomes,%and%this%fiber%is%wrapped%into%higher%order%structures%up%to%the%level%of%a%chromosome%– “chroma,n”%refers%to%the%structure%of%DNA%+%nucleosomes%– Each%nucleosome%is%an%octamer%composed%of%4%pairs%of%different%histone%proteins:%H2A,%
H2B,%H3,%and%H4%
hbps://www.broadins,tute.org/files/news/images/2010/chroma,n_states_2a.png%
hbp://www.mun.ca/biology/desmid/brian/BIOL2060/BIOL2060"18/1820.jpg%
Courtesy of the Broad Institute. Used with permission. The most recent best practicescan be found at this website: https://www.broadinstitute.org/gatk/guide/best-practices.
© Pearson Education, Inc. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
4
| yHistone modification
or variantSignal
characteristicsPutative functions
H2A.Z Peak Histone protein variant (H2A.Z) associated with regulatory elements with dynamic chromatinH3K4me1 Peak/region Mark of regulatory elements associatedwithenhancersandotherdistal elements,but alsoenricheddownstreamof transcription startsH3K4me2 Peak Mark of regulatory elements associated with promoters and enhancersH3K4me3 Peak Mark of regulatory elements primarily associated with promoters/transcription startsH3K9ac Peak Mark of active regulatory elements with preference for promoters
H3K9me1 Region Preference for the 59 end of genesH3K9me3 Peak/region Repressive mark associated with constitutive heterochromatin and repetitive elementsH3K27ac Peak Mark of active regulatory elements; may distinguish active enhancers and promoters from their inactive counterparts
H3K27me3 Region Repressive mark established by polycomb complex activity associated with repressive domains and silent developmental genesH3K36me3 Region Elongation mark associated with transcribed portions of genes, with preference for 39 regions after intron 1H3K79me2 Region Transcription-associated mark, with preference for 59 end of genesH4K20me1 Region Preference for 59 end of genes
Histone%modifica,ons%– Par,cular%residues%on%the%tails%of%these%histones%commonly%undergo%
post"transla,onal%chemical%modifica,ons%
%
hbp://a.sta,c"abcam.com/CmsMedia/Media/common"histone"modifica,on"1.jpg%
– Some%of%these%modifica,ons%are%associated%with%func,ons%–%different%combina,ons%of%marks%and%their%meaning%compose%the%“histone%code”%
%
ENCODE%Consor,um%Nature%2012%
Most%common%in%papers%
© Abcam. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
Courtesy of Macmillan Publishers Limited. Used with permission.Source: ENCODE Project Consortium. "An Integrated Encyclopedia of DNA Elements in the Human Genome." Nature 489, no. 7414 (2012): 57-74.
5
• In%addi,on%to%histone%modifica,ons,%gene%expression%can%be%affected%by%DNA%methyla,on:%the%5%carbon%of%cytosines%in%DNA%can%be%methylated.%– In%metazoans,%only%C’s%before%G’s%can%be%methylated%
(the%C’s%of%CpG).%Hundred%or%thousands%of%base"long%stretches%rich%in%methylated%cytosines%form%“CpG%islands”%at%some%promoters%to%repress%gene%expression%
• “Epigene,c”%changes%are%changes%to%DNA%not%at%the%level%of%primary%sequence%which%are%reversible%&%heritable%
• Epigene,c%marks%are%ohen%cell"type%and/or%disease%state"specific%– For%example,%the%pluripotency%gene%Nanog%is%%
%demethylated%during%reprogramming%of%differen,ated%%cells%into%iPSCs%
• Enzymes%ac,vely%regulate%the%epigene,c%marks%– Chroma,n%modifiers%and%nucleosome%remodelers%are%enzymes%
that%ac,vely%regulate%chroma,n%marks,%nucleosome%posi,oning%&%turnover%
– DNA%methyltransferases%to%methylate%DNA%
Histone%code%&%DNA%methyla,on%regulate%gene%expression%
Courtesy of Macmillan Publishers Limited. Used with permission.
6
Profiling%histone%modifica,ons%• ChIP"seq%w/%an,bodies%specific%to%a%par,cular%type%of%modified%
nucleosome%can%map%histone%modifica,ons%genome"wide%
• We’d%like%to%come%up%with%a%way%to%combine%these%combina,ons%of%histone%marks%throughout%the%genome%into%func,onal%annota,ons%%• Based%on%an%observed%pabern%of%marks%at%a%locus,%we’d%like%to%label%it%w/%
‘enhancer’,%‘promoter’,%‘inac,ve’%or%‘ac,ve%gene%body%region’,%etc.%
• 2%approaches%to%func,onal%annota,on%of%the%genome:%%"%Hidden%Markov%Model%(ChromHMM)%%"%Dynamic%Bayesian%Network%(Segway)%
%%
7
Dynamic%Bayesian%Networks%• A%Bayesian%network%(directed%graphical%model%where%arcs/edges%represent%condi,onal%dependencies)%that%models%a%dynamic%process%(sequen,al%data,%either%temporal%or%spa,al%–%e.g.%along%the%genome)%
• Similar%to%Hidden%Markov%Models,%but%include%addi,onal%random%variables%that%allow%tuning%(e.g.,%hard%limits%on%segment%lengths)%
8
Segway:%Dynamic%Bayesian%Network%
∈
Variable’s%parents%are%indicated%by%its%direct%predecessor%in%the%directed%graph%%Every%variable%is%condi,onally%independent%of%all%variables%in%the%model%given%its%parents**n%observa,on%tracks%T:%sequence%length%%Square:%discrete%random%variable%Circle:%con,nuous%random%variable%%White:%hidden%variable%Black:%observed%variable%
Black%arcs%(edges)%=%determinis,c%condi,onal%dependence,%red%=%stochas,c%condi,onal%dependence%
) ) )( ( ( (
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) )) )
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9
Segway:%Dynamic%Bayesian%Network%
∈Observa,on%track:%assay%output%(e.g.,%density%of%H3K4me3%ChIP"seq%reads%–%one%track%for%each%of%n%experiments)%%
Indicator:%1/0%whether%or%not%the%assay%produced%any%results%for%that%region%(=0%if%assay%can’t%map%reads%to%that%region.%In%this%case,%the%edge%from%Qt%to%Xt(i)%is%edited%out)%%
Segment%label:%The%hidden%annota,on%you’re%trying%to%infer%(e.g.%promoter).%
) ) )
( ( ( (
)
) )) )
) )) )
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© source unknown. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
10
Segway:%Dynamic%Bayesian%Network%
∈
Countdown:%Discrete%variable%that%allows%the%specifica,on%of%minimum%or%maximum%segment%length.%Starts%at%ini,al%value%dependent%on%QT%(might%want%TSS%to%be%short%but%intergenic%region%to%be%long)%and%decreases%where%ruler%marker%MT=1.%%
Ruler%marker:%%=1%every%10th%posi,on,%0%
otherwise%(every%10th%posi,on,%we%update%the%countdown%variable%as%to%how%long%we’ve%been%in%that%label)%
) ) )
( ( ( (
)
) )) )
) )) )
)) )
) )))
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( ( ( (
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)) )
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) )
© source unknown. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
11
Segway:%Dynamic%Bayesian%Network%
∈
Transi,on:%binary%segment%transi,on%label%that%either%forces%the%segment%label%to%change%at%the%current%posi,on%(Jt=1)%or%prevent%it%from%changing%(Jt=0).%
Segway%generates%a%condi,onal%probability%table%P(Jt=1|Qt"1,Ct"1)%that%maps%each%(Qt"1,Ct"1)%to%one%of%three%rules%that%determine%the%value%of%Jt:%
%1.%Force:%P(Jt=1)%=%1%%2.%Prevent:%P(Jt=1)%=%0%%3.%Allow:%P(Jt=1)=1/(1+L)%
“Allow”%rule%models%geometric%distribu,on%w/expected%length%L%
) ) )
( ( ( (
)
) )) )
) )) )
)) )
) )))
) )
) ) )
( ( ( (
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) )) )
) )) )
)) )
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) )
© source unknown. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
12
• Train%on%1%%of%the%Genome%– Assign%equal%probability%(=1/n)%of%each%label%to%the%star,ng%posi,on,%then%use%
Expecta,on"Maximiza,on%(EM)%algorithm%to%learn%model%parameters%(contribu,ons%of%each%track%(experimental%assay)%to%each%label)%%
– Star,ng%from%different%ini,al%condi,ons%(i.e.,%contribu,ons%of%each%track%to%a%par,cular%label)%gave%similar%results%
• Then%use%these%parameters%to%segment%the%rest%of%the%genome%using%Viterbi%decoding%(similar%to%what%we%discussed%for%HMMs)%
Segway:%Dynamic%Bayesian%Network%
13
Window position
33046000 33047000ScaleChr6:
DL0
F0F1R0R1R2R3R4R5C0
H3K9me1TF0TF1TF2TSSGS
E/GMGM0GM1GE0GE1GE2
HLA-DMAHLA-DMA
BRD2
BRD2
BRD2BRD2
BRD2
BRD2
BRD2
AL645941.1BRD2
BRD2BRD2
BRD2
BRD2BRD2
C1
L1
33048000 33049000 33050000 33051000Segway 31-track chromatin segmentation (K562)
ENCODE Gencode Manual Gene Annotations (level 1+2) (Oct 2009)
Human Mar. 2006 (NCBI36/hg18)5 kb
chr6:33044414-33057260 (12,847 bp)
33052000 33053000 33054000 33055000 33056000 33057000
"Arbitrarily%chose%there%to%be%25%labels%(so%that%they%would%remain%interpretable%by%biologists)%%The%authors%gave%names%to%the%resul,ng%25%labels:%% %D:%“dead”%–%no%ac,vity%% %GS:%gene%start%% %GM:%gene%middle%% %GE:%gene%end%% %E:%enhancer%%%
Example%of%Segway’s%segmenta,on%for%a%gene%
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14
Transcrip,on%Factor%Binding%• Many%more%possible%binding%sites%in%genome%than%are%actually%occupied%• Binding%sites%are%different%in%cell%types%and%across%,me%
) ) )
~650,000(((((TF(Mo/fs)
~50,000(binding(sites(for(a(typical(TF)
( ( ( ( ( ( ( ( ( (( ( (
Mo/fs(are(insufficient(to(predict(binding(
Binding(sites(change(across(/me(
• One%key%determinant%of%whether%or%not%a%TF%binds%is%the%local%chroma,n%landscape:%is%the%DNA%accessible?%
15
Dnase"seq%reveals%protected%regions%of%the%genome%
• DNase"I%cleaves%at%unprotected%regions%– Regions%of%open%chroma,n%– Not%wrapped%around%nucleosomes%or%bound%strong%by%TFs%
) ) )
( ( ( ( (
(175)–)400bp))
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16
Protein%Interac,on%Quan,ta,on%(PIQ)%• Predicts%TF%binding%from%DNase"seq%+%sequence%mo,f%preferences%of%TFs%
• Can%get%predic,ons%for%hundreds%of%TFs%(need%a%mo,f%for%that%TF)%–%no%need%for%an,bodies%specific%to%proteins%
) ) )
( ( ( ( ( (( ( ( ( (
;( ;(…(
Input:)
Modeling:)
Predic'ons:)Courtesy of Macmillan Publishers Limited. Used with permission.Source: Sherwood, Richard I., Tatsunori Hashimoto, et al. "Discovery of Directional and Nondirectional PioneerTranscription Factors by Modeling DNase Profile Magnitude and Shape." Nature Biotechnology 32, no. 2 (2014): 171-8.
17
) ) )
( ( ( ((( (
) ) ) ) ) ) ) )) )
)) ) ) ) ) ) ) ) )
) )
3%Steps%of%PIQ%algorithm%• 1.%Iden,fica,on%of%candidate%sites%using%TF%mo,fs%from%TF%
databases%
• 2.%Smoothing%of%raw%reads%from%each%DNase"seq%experiment.%DNase"seq%reads%are%modeled%as%arising%from%a%Gaussian%process%to%remove%noise%by%adap,vely%smoothing%the%reads%from%neighboring%bases%
• 3.%Iden,fy%binding%sites%of%TF%by%itera,vely%combining%direct%evidence%of%binding%(DNase"seq)%with%computer"generated%model%of%DNaseI%hypersensi,vity%that%includes%that%event%(uses%TF"signature%profile%shapes%and%magnitudes%for%each%TF%to%build%a%model%of%the%expected%DNaseI%hypersensi,vity)%
• Use%log"likelihood%ra,o%to%test%each%region%for%TF%binding,%calling%those%above%1%%of%null%distribu,on%as%binary%“bound”%regions%
18
Pioneer%Transcrip,on%Factors%• Region%of%“closed”%chroma,n%that’s%inaccessible%to%most%TFs%can%be%opened%by%pioneer%TF%binding%
• Then%once%chroma,n%is%opened,%other%“sebler”%TFs%can%bind%
) ) )
( ( ( ( ( (
) ) ) ) ) ) ) ) ) ) ) ) ) )
) ) ) ) ) ) ) ) )
) ) ) ) ) )
)
)
Zaret)2011)© Cold Spring Harbor Laboratory Press. All rights reserved. This content is excluded from ourCreative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.Source: Zaret, Kenneth S., and Jason S. Carroll. "Pioneer Transcription Factors: EstablishingCompetence for Gene Expression." Genes & Development 25, no. 21 (2011): 2227-41.
19
Iden,fica,on%of%Pioneer%TFs%• Apply%PIQ%to%a%developmental%lineage%model%that%involves%stepwise%differen,a,on%of%mouse%stem%cells%– Collect%DNase"seq%data%at%six"cell%states%at%different%,mepoints%– “Pioneer%index”%measures%mo,f"specific%expected%increase%in%DNaseI%
accessibility%at%sites%whose%binding%changes%at%successive%,mepoints%– Most%mo,fs%showed%lible%pioneer%ac,vity,%while%a%small%number%of%mo,fs%
(TFs)%open%chroma,n%substan,ally%upon%binding%
– Sebler%TFs%can%bind%once%pioneers%have%opened%the%chroma,n;%loss%of%pioneer%binding%causes%chroma,n%to%return%to%a%closed%state%
mESCs (day 0)
Serum removalWntAct + Activin
Bmp
WntAct RA + Bmp+ Tgf inh
ActivinBmpinh
Mesendoderm(day 3)
Mesoderm(day 5)
Endoderm(day 5)
Intestinalendoderm
(day 6)
Prepancreaticendoderm
(day 6)
a
120
100
80
60
40
20
0–3 –1 1 3 5 7 9 11 13 15
Num
ber
of T
Fs
Pioneer index score
c
d
t0
t1
Oct
4, R
XR
:RA
R, M
yc
Fox
A
CR
EB
Klf/
Sp,
ET
SN
FY
A, E
2F
Nrf
1Z
fp16
1
KA
ISO
Motif
Motif
Pioneer
Courtesy of Macmillan Publishers Limited. Used with permission.Source: Sherwood, Richard I., Tatsunori Hashimoto, et al. "Discovery of Directional and Nondirectional PioneerTranscription Factors by Modeling DNase Profile Magnitude and Shape." Nature Biotechnology 32, no. 2 (2014): 171-8.
20
Asymmetrical%chroma,n%opening%by%direc,onal%pioneers%
• For%non"palindromic%mo,fs%(e.g.%AATTCG),%we%know%which%strand%(+/")%the%mo,f%is%on%and%therefore%in%which%direc,on%the%TF%is%binding%
• Some%pioneer%TFs%tend%to%open%chroma,n%more%strongly%in%one%direc,on%–%could%inform%mechanisms%of%pathways%how%TFs%deposit%histone%marks%
Creb1a
Klf7 NFYA Zfp161
Chr
omat
in
open
ing
Inde
x
Motif Motif Motif Motif
21
3D%structure%of%the%genome%&%enhancer%looping%
• DNA%is%packaged%,ghtly%in%3D%space%in%the%nucleus%– This%structure%dictates%which%elements%far%apart%on%the%genome%(Mb%away)%
can%physically%interact%due%to%close%proximity%in%3D%space%• Important%for%forma,on%of%promoter"enhancer%interac,ons%
– Enhancers:%distal%regulatory%elements%that,%when%bound%by%specific%TFs,%enhance%the%expression%of%an%associated%gene%
hbp://www.science.ngfn.de/images/S31T04_fig1.JPG% hbp://www.nature.com/nrg/journal/v15/n4/images/nrg3663"f4.jpg%
© Michael Speicher. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
Courtesy of Macmillan Publishers Limited. Used with permission.Source: Ong, Chin-Tong, and Victor G. Corces. "CTCF: An Architectural ProteinBridging Genome Topology and Function." Nature Reviews Genetics (2014).
22
ChIA"PET%reveals%3D%interac,ons%of%the%genome%
"Abach%linkers%w/%restric,on%enzyme%sites%&%perform%liga,on%in%dilute%condi,ons%to%favor%liga,on%within%each%complex%
hbp://genomebiology.com/content/figures/gb"2010"11"2"r22"1"l.jpg%
"Crosslink%DNA%&%proteins,%ChIP%on%protein%of%interest%(e.g.%RNA%Pol%II),%and%shear%DNA%
"%Perform%restric,on%digest%&%PCR%amplify%fragments,%then%sequence%
" Two%types%of%liga,on%events:%1.%Self"liga,on%(e.g.,%both%tags%are%near%the%promoter)%–%these%map%near%each%other%on%the%genome%&%we%throw%these%out%2.%Inter"liga,on%(e.g.,%1%tag%from%promoter%&%1%from%enhancer)%reveal%interac,ons%
Chroma,n%Interac,on%Analysis%by%Paired"End%Tagging%
hbp://www.nature.com/nature/journal/v462/n7269/images/nature08497"f1.2.jpg%
Courtesy of Macmillan Publishers Limited. Used with permission.Source: Fullwood, Melissa J., Mei Hui Liu, et al. "An Oestrogen-receptor-α-boundHuman Chromatin Interactome." Nature 462, no. 7269 (2009): 58-64.
Courtesy of Li et al. License: CC-BY.Source: Li, Guoliang, Melissa J. Fullwood, et al. "Software ChIA-PET Tool for ComprehensiveChromatin Interaction Analysis with Paired-end Tag Sequencing." Genome Biology 11 (2010): R22
23
ChIA"PET%reveals%3D%interac,ons%of%the%genome%
"ChIA"PET%sequence%tags%that%pair%with%tags%from%known%promoter%regions%reveal%RNA%PolII%ChIP%peaks%that%are%at%enhancer%regions%
hbp://www.nature.com/ng/journal/v45/n8/images/ng.2677"F2.jpg%
Courtesy of Macmillan Publishers Limited. Used with permission.Source: Mercer, Tim R., Stacey L. Edwards, et al. "DNase I-hypersensitive ExonsColocalize with Promoters and Distal Regulatory Elements." Nature Genetics (2013).
24
Assessing%significance%of%ChIA"PET%interac,ons%
• Inter"liga,on%events%(e.g.%between%a%puta,ve%enhancer%and%promoter)%could%arise%from%two%sources%– 1.%Within%the%same%cluster%–%these%are%true%3D%interac,ons%– 2.%From%liga,on%between%2%different%clusters%–%these%are%false%posi,ves%
• We%need%to%assess%if%the%inter"liga,on%events%are%significantly%enriched%for%having%occurred%from%within%the%same%cluster%(true%interac,on%events)%
hbp://genomebiology.com/2010/11/2/R22/figure/F1%
Courtesy of Li et al. License: CC-BY.Source: Li, Guoliang, Melissa J. Fullwood, et al. "Software ChIA-PET Tool for ComprehensiveChromatin Interaction Analysis with Paired-end Tag Sequencing." Genome Biol 11 (2010): R22.
25
Assessing%significance%of%ChIA"PET%interac,ons%
• Hypergeometric%test%for%significance%– IA,B:%#%of%inter"liga,on%events%between%loci%A%and%B%(paired"tags%mapping%to%A%
&%B)%
– cA%,%cB:%total%number%of%liga,on%events%associated%with%A%,%B%(single%tags%mapping%to%A%or%B)%
– N:%total%number%of%liga,on%events%(total%single%tags)%
) ) )
( ( ( ( ( ( ( (( ( ( ( ( ( ( ( ( ( (
( (
P (IA,B |N, cA, cB) =
(cA
IA,B
)(NcA
cBIA,B
)
(NcB
)
) ) )
( ( ( ( ( ( ( (( ( ( ( ( ( ( ( ( ( (
( (
p =
min{cA,cB}X
i=IA,B
P (i|N, cA, cB)P"value%is%probability%of%your%observa,on%plus%anything%more%extreme:%
Probability%of%observing%exactly%your%observed%number%of%inter"liga,on%events%under%null%hypothesis%that%each%s,cky%end%has%an%equal%probability%of%liga,ng%to%any%other%end:%
26
ChIA"PET%has%a%high%false%nega,ve%rate%
• Due%to%heterogeneous%star,ng%popula,on%of%cells%(transient%promoter"enhancer%interac,ons),%complex%protocol%&%stringent%P"values%to%cut%down%on%false"posi,ves,%ChIA"PET%has%a%high%false%nega,ve%rate%
• So,%given%an%a%number%of%promoter"enhancer%interac,ons%observed%in%ChIA"PET%experiment%1%&%in%ChIA"PET%experiment%2%with%each%capturing%only%a%subset%of%the%total%events,%we’d%like%to%es,mate%the%true%number%of%interac,ons%occurring%in%the%cell%
27
Es,ma,ng%the%total%number%of%events%from%overlap%
• Again,%we%can%use%the%hypergeometric%model%– Given%two%observed%sample%sizes%m%&%n%along%with%their%overlap%k,%we’d%like%to%es,mate%the%total%number%events%N*
– The%maximum%likelihood%es,mate%of%N%is%approximately:%
– Example:%Experiment%1:%100%events%% % %Experiment%2:%200%events%% % %"%overlap%is%only%20.%It%seems%like%we%must%be%sampling%
only%a%small%frac,on%of%the%total%events%each%,me!%%"%Indeed,%maximum%likelihood%es,mate%is%1000%total%events%that%
each%sample%came%from%
) ) )
( ( ( ( (
) ) ) ) ) ) ) )) ) ) ) ) ) ) ) )
) ) )) ) ) ) ) ) ) ) ) )
) ) ) ) ) ) ) ) % )) ) ) ) )
))
) ) ) ) ) ) ) )))
) ) )
( ( ( ( ( (( ( (
) ) ) ) % ) ))
) ) ) ) ) ) ) ) ) )) ) ) ) ) )
) ) )
28
• The%previous%model%assumes%all%events%were%true%posi,ves,%while%in%reality%some%are%false%posi,ves.%– We%overes,mate%the%total%event%count%since%the%observed%m%and%n%are%larger%than%they%truly%are%without%the%false%posi,ves%
– Assume%the%overlapping%events%are%true%posi,ves%and%the%non"overlapping%events%have%false%posi,ve%rate%f%(so%1"f%of%the%events%are%true%posi,ves).%Then%we%can%update%es,mates%of%m%and%n:%
– With%the%previous%example%(100%and%200%events%w/%20%overlapping),%let’s%say%there%is%a%false%posi,ve%rate%of%5%.%Then:%• m’%=%(0.95)(80)%+%20%=%96%• n’%=%(0.95)(180)%+%20%=%191%• The%modified%es,mate%of%the%total%#%of%events%if%therefore:%
(96)(191)/20%≈%869%(vs.%1000%without%considering%false"posi,ves)%
*
Es,ma,ng%the%total%number%of%events%from%overlap%
) ) )
( ( ( ( (
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) ) ) ) ) ) ) ) )
) ) ) ) ) ) ) % ) ) )) ) ) ) ) ) ) )
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MIT OpenCourseWarehttp://ocw.mit.edu
7.91J / 20.490J / 20.390J / 7.36J / 6.802J / 6.874J / HST.506J Foundations of Computational and Systems BiologySpring 2014
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